Riemann Hypothesis, Matrix/Gravity Correspondence and FZZT Brane Partition Functions
| dc.creator | McGuigan, Michael | |
| dc.date | 2007-08-06 | |
| dc.date.accessioned | 2026-07-07T08:22:15Z | |
| dc.date.available | 2026-07-07T08:22:15Z | |
| dc.description | We investigate the physical interpretation of the Riemann zeta function as a FZZT brane partition function associated with a matrix/gravity correspondence. The Hilbert-Polya operator in this interpretation is the master matrix of the large N matrix model. Using a related function $Ξ(z)$ we develop an analogy between this function and the Airy function Ai(z) of the Gaussian matrix model. The analogy gives an intuitive physical reason why the zeros lie on a critical line. Using a Fourier transform of the $Ξ(z)$ function we identify a Kontsevich integrand. Generalizing this integrand to $n \times n$ matrices we develop a Kontsevich matrix model which describes n FZZT branes. The Kontsevich model associated with the $Ξ(z)$ function is given by a superposition of Liouville type matrix models that have been used to describe matrix model instantons. | |
| dc.description | 17 pages, 2 figures, 1 table | |
| dc.identifier | https://arxiv.org/abs/0708.0645 | |
| dc.identifier | http://arxiv.org/abs/0708.0645 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135591 | |
| dc.subject | Mathematical Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Riemann Hypothesis, Matrix/Gravity Correspondence and FZZT Brane Partition Functions | |
| dc.type | text |